The optimal antenna weighting scheme that minimizes the average bit error rate in a closed-loop transmit antenna diversity system is investigated under the assumption that channel state information is provided at both the transmitter and the receiver. A closed-form expression for the optimal transmitter weights is derived with a fixed average transmit power constraint. Also, the effect of limited peak transmit power on the performance of the optimal weighting method is analyzed. Base on this analysis, it is shown that the proposed transmitter weights yield significant performance improvements over the conventional weights on the wide range of practical system parameters.